Binary Phase Shift Keying (BPSK) is a popular modulation scheme wherein information bits are encoded as +1 or −1. For channels where the main source of signal distortion is through additive white Gaussian noise (AWGN), the optimal (in terms of minimum error probability) operations to be performed at the receiver are well known. However, in a typical wireless channel, such a transmitted signal undergoes distortion due to fading and path loss in addition to additive noise and interference.
Such fading channels are characterized not only by rapid amplitude and phase variations but also time and/or frequency dispersion. This poses a problem in the demodulation of phase or frequency modulated signals. The fading channel causes rapid changes in the phase thus making it very difficult to infer the phase of the received signal from the modulated data symbols. Different solutions for this problem have been used in second and third generation wireless systems. These include non-coherent detection, differential detection, pilot signal and pilot symbol assisted schemes. While each scheme provides a mechanism for either not requiring knowledge of the exact phase at the receiver or inferring it more accurately, there is an associated loss in performance. For example, non-coherent and differential modulation result in an increase in the required signal-to-noise ratio (SNR) compared to coherent schemes; pilot signal based schemes lead to a loss in power available for the information bits; and pilot symbol based schemes lead to a loss in bandwidth and power available for information bits.
Of the above-mentioned solutions, Pilot Symbol Assisted Modulation (PSAM) has received much attention in recent years. PSAM will be part of the wideband CDMA (Code Division Multiple Access) standard of the universal mobile telecommunications system (UMTS) being studied by the 3rd Generation Partnership Project (3GPP). (3GPP is a standards body comprising the European Telecommunication Standards Institution (ETSI) and several other international standards bodies.)
The basic idea behind PSAM is to periodically insert symbols known to the receiver in the information bit stream. If the pilot symbols are inserted often enough, they can be used to estimate the channel fading conditions and therefore can be used to coherently (i.e., with knowledge of the phase rotation introduced by the channel) demodulate the information bits. Since pilot symbols are corrupted by noise, the estimates of the fading conditions are not exact and hence the available information is insufficient to determine the optimal receiver. If the statistics (probability density function, in particular) of the fading are known, then one can derive the optimal operations to be performed at the receiver for detecting the transmitted bit. The form of such a receiver is known in the art. Unfortunately, when nothing is known about the fading statistics, or fading distribution, (as is typically the case) then this form of the receiver no longer provides an optimal solution.